Question

If "F" is the magnitude of resultant b/w two forces "F", then the angle b/w the forces is: a) 20° b) 120° c) 60° d) 210°​

Answer 1

hmm interesting

$f \: = \sqrt{a {}^{2} + {b}^{2} + 2ab \cos( \alpha ) }$

$\bold{now \: \: given \: magnitude \: of \: force = f \: and \: resultant \: = \: f}$

$f = \sqrt{ {f}^{2} + {f}^{2} + 2(f)(f) \cos( \alpha ) }$

$f = \sqrt{2 {f}^{2} + 2 {f}^{2} \cos( \alpha ) } \\ \\ {f}^{2} = 2 {f}^{2} + 2 {f}^{2} \cos( \alpha )$

${f}^{2} - 2{f}^{2} = 2 {f}^{2} \cos( \alpha ) \\ \\ \frac{ - {f}^{2} }{2 {f}^{2} } = \cos( \alpha ) \\ \\ \frac{ - 1}{ \: \: 2} = cos \alpha \\ \\ \alpha = { \cos }^{ - 1} \frac{ - 1}{2} \: {inverse \: trigonometric \: rule}\\ \\ \alpha = 120$